IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1603.09324.html
   My bibliography  Save this paper

Parisian ruin for a refracted L\'evy process

Author

Listed:
  • Mohamed Amine Lkabous
  • Irmina Czarna
  • Jean-Franc{c}ois Renaud

Abstract

In this paper, we investigate Parisian ruin for a L\'evy surplus process with an adaptive premium rate, namely a refracted L\'evy process. More general Parisian boundary-crossing problems with a deterministic implementation delay are also considered. Our main contribution is a generalization of the result in Loeffen et al. (2013) for the probability of Parisian ruin of a standard L\'evy insurance risk process. Despite the more general setup considered here, our main result is as compact and has a similar structure. Examples are provided.

Suggested Citation

  • Mohamed Amine Lkabous & Irmina Czarna & Jean-Franc{c}ois Renaud, 2016. "Parisian ruin for a refracted L\'evy process," Papers 1603.09324, arXiv.org, revised Mar 2017.
    • Handle: RePEc:arx:papers:1603.09324
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1603.09324
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. David Landriault & Jean-François Renaud & Xiaowen Zhou, 2014. "An Insurance Risk Model with Parisian Implementation Delays," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 583-607, September.
    2. Loeffen, Ronnie L. & Renaud, Jean-François & Zhou, Xiaowen, 2014. "Occupation times of intervals until first passage times for spectrally negative Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 124(3), pages 1408-1435.
    3. Landriault, David & Renaud, Jean-François & Zhou, Xiaowen, 2011. "Occupation times of spectrally negative Lévy processes with applications," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2629-2641, November.
    4. Wong, Jeff T.Y. & Cheung, Eric C.K., 2015. "On the time value of Parisian ruin in (dual) renewal risk processes with exponential jumps," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 280-290.
    5. Ronnie Loeffen & Irmina Czarna & Zbigniew Palmowski, 2011. "Parisian ruin probability for spectrally negative L\'{e}vy processes," Papers 1102.4055, arXiv.org, revised Mar 2013.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mohamed Amine Lkabous, 2019. "A note on Parisian ruin under a hybrid observation scheme," Papers 1907.09993, arXiv.org.
    2. Irmina Czarna & Adam Kaszubowski, 2020. "Optimality of Impulse Control Problem in Refracted Lévy Model with Parisian Ruin and Transaction Costs," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 982-1007, June.
    3. David Landriault & Bin Li & Mohamed Amine Lkabous, 2019. "On occupation times in the red of L\'evy risk models," Papers 1903.03721, arXiv.org, revised Jul 2019.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Landriault, David & Li, Bin & Wong, Jeff T.Y. & Xu, Di, 2018. "Poissonian potential measures for Lévy risk models," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 152-166.
    2. Lkabous, Mohamed Amine & Czarna, Irmina & Renaud, Jean-François, 2017. "Parisian ruin for a refracted Lévy process," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 153-163.
    3. Guérin, Hélène & Renaud, Jean-François, 2017. "On the distribution of cumulative Parisian ruin," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 116-123.
    4. Landriault, David & Li, Bin & Lkabous, Mohamed Amine, 2020. "On occupation times in the red of Lévy risk models," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 17-26.
    5. Czarna, Irmina & Renaud, Jean-François, 2016. "A note on Parisian ruin with an ultimate bankruptcy level for Lévy insurance risk processes," Statistics & Probability Letters, Elsevier, vol. 113(C), pages 54-61.
    6. Li, Shu & Zhou, Xiaowen, 2022. "The Parisian and ultimate drawdowns of Lévy insurance models," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 140-160.
    7. Lkabous, Mohamed Amine, 2019. "A note on Parisian ruin under a hybrid observation scheme," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 147-157.
    8. Cheung, Eric C.K. & Wong, Jeff T.Y., 2017. "On the dual risk model with Parisian implementation delays in dividend payments," European Journal of Operational Research, Elsevier, vol. 257(1), pages 159-173.
    9. Cui, Zhenyu & Nguyen, Duy, 2016. "Omega diffusion risk model with surplus-dependent tax and capital injections," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 150-161.
    10. Xiaoqing Liang & Virginia R. Young, 2020. "Minimizing the Probability of Lifetime Exponential Parisian Ruin," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 1036-1064, March.
    11. Brinker, Leonie Violetta & Eisenberg, Julia, 2021. "Dividend optimisation: A behaviouristic approach," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 202-224.
    12. David Landriault & Bin Li & Mohamed Amine Lkabous, 2019. "On occupation times in the red of L\'evy risk models," Papers 1903.03721, arXiv.org, revised Jul 2019.
    13. Landriault, David & Li, Bin & Lkabous, Mohamed Amine, 2021. "On the analysis of deep drawdowns for the Lévy insurance risk model," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 147-155.
    14. Mohamed Amine Lkabous, 2019. "Poissonian occupation times of spectrally negative L\'evy processes with applications," Papers 1907.09990, arXiv.org.
    15. Landriault, David & Li, Bin & Lkabous, Mohamed Amine & Wang, Zijia, 2023. "Bridging the first and last passage times for Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 308-334.
    16. Mohamed Amine Lkabous, 2019. "A note on Parisian ruin under a hybrid observation scheme," Papers 1907.09993, arXiv.org.
    17. Yang, Chen & Sendova, Kristina P. & Li, Zhong, 2020. "Parisian ruin with a threshold dividend strategy under the dual Lévy risk model," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 135-150.
    18. Lkabous, Mohamed Amine & Wang, Zijia, 2023. "On the area in the red of Lévy risk processes and related quantities," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 257-278.
    19. Albrecher, Hansjörg & Ivanovs, Jevgenijs, 2017. "Strikingly simple identities relating exit problems for Lévy processes under continuous and Poisson observations," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 643-656.
    20. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, December.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1603.09324. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.